how do you rotate a function to a certain angle?
say
y = x^2+1 to 45degree

Question

how do you rotate a function to a certain angle?
say
y = x^2+1 to 45degree

anonymous · Answer

you can draw a new XY coodinate system and center the graph about the line y=x|dw:1333574057443:dw|

anonymous · Answer

I think you want the new equation also huh?

anonymous · Answer

Well, that would require a bit more work...

anonymous · Answer

well yes, of course, so any help?

kinggeorge · Answer

One of a couple problems that I'm seeing, is that $x^2+1$ isn't a function anymore if you rotate it even the tiniest bit.

anonymous · Answer

ok yes it would be broken into various funtions, so how are they?

kinggeorge · Answer

I suppose one option would be to simply change the basis/variables. You can create new variables s, t such that the s axis is 45 degrees off the positive x-axis and the t axis is 45 degrees off the positive y-axis. Then write you equation as $t=s^2+1$ and convert back to x, y after that.

kinggeorge · Answer

You would still run into problems about the domain when converting though.

kinggeorge · Answer

I think your change of variables would look something like $$s=\sqrt{2x^2}$$$$t=\sqrt{2y^2}$$

anonymous · Answer

I don't think that will do

kinggeorge · Answer

Not that I disagree with you, but why won't it work?

anonymous · Answer

never mind, I have found an answer

kinggeorge · Answer

Out of curiosity, what was it?

anonymous · Answer

first there is: x^2 - 2xy + y^2 - x * sqrt(2) - y * sqrt(2) = 0
and when solved for y there is:
y = [(sqrt(2) + 2x) +/- sqrt(4x^2 + 2 + 4 sqrt(2) x - 4x^2 + 4 sqrt(2) x)] / 2

or

y = [sqrt(2) + 2x +/- sqrt(8 sqrt (2) x + 2)]/2.